# Identify Direct Proportion and Solve Simple Problems

In this worksheet, students will be able to calculate best value for money and solve proportion problems.

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR

Curriculum topic:   Ratio, Proportion and Rates of Change

Curriculum subtopic:   Ratio, Proportion and Rates of Change, Discrete Growth and Decay

Difficulty level:

### QUESTION 1 of 10

The best way to solve all problems involving direct proportion is to start by finding the single unit value

Before solving any direct proportion problem, think carefully about it to make sure you know how to find the single unit value.

If 8 pens cost £5.28, what is the cost of 5 pens?

We need to find the cost of 1 pen.

 Pens Cost 8 £5.28 1 £5.28 ÷ 8 £0.66 5 £0.66 x 5 £3.30

12 blocks of cheese make sandwiches for 48 people. How many  people can sandwiches can be made from 30 blocks of cheese?

Find out how many sandwiches can be made from 1 block of cheese.

1 block will make 48 ÷12 = 4 sandwiches

30 blocks of cheese will make

30 x 4 = 120 people

Now you have a pen and a cheese sandwich it is time to try out some activities.

What is the cost of 60 eggs when  12 eggs can be bought for £2.10?

£10.25

£9.75

£10.60

£10.50

If 8 cans of fizzy drinks cost  £5.60, what do 5 cans cost?

£3.50

£4.30

£3.75

£4.25

If 12 litres of paint cost £45, how much does the following cost?

Show all answers to 2 decimal places (2 d.p)

£3.50

£4.30

£3.75

£4.25

If 8 of the same DVD's cost £96, how many DVD's can be bought for £60?

Mindy buys 12 pens for  £7.80 and 6 note books for  £10.50.  How much does Mindy pay altogether for 7 pens and 4 note books?

Here is a recipe for a fruit cake that serves 6 people.

175 g dried fruit

50 g candied peel

120 ml water

175 g butter

180 g caster sugar

3 large eggs

450 g flour

How much flour is required for  a cake to feed 11 people?

How many eggs are required for a cake to feed 16 people?

Tracey changed £50 into dollars for her holiday to America.  The exchange rate was £1 = \$1.55

How many dollars did Tracey have at the start of her holiday?

Tracy came back with \$30.  How much did she get back in Pounds?

A lorry uses 35 litres of fuel to travel 250 km.

A farm shop sells apples for £9 for a 12.5kg bag.

The same apples cost £1.83 for a 2.5kg bag at the supermarket.

Where are the apples better value, at the farm shop or the supermarket?

The Coffee Cabin sells coffee in three different size cups.

£2.25 for 175 ml

£2.75 for 250 ml

£375 for 300 ml

Which size cup of coffee is the best value for money?

• Question 1

What is the cost of 60 eggs when  12 eggs can be bought for £2.10?

£10.50
EDDIE SAYS
Find the cost of one egg. £2.10 ÷ 12 = 0.175 (do not round up) 0.175 x 60 = £10.50 You may have noticed that 12 x 5 = 60 so you could have just done £2.10 x 5 = £10.50. Just to scramble your brain so early on in the activity..
• Question 2

If 8 cans of fizzy drinks cost  £5.60, what do 5 cans cost?

£3.50
EDDIE SAYS
£5.60 ÷ 8 = 0.70 0.70 x 5 = £3.50 If you are not sure which way round to divide always start with the money and divide by the number given.
• Question 3

If 12 litres of paint cost £45, how much does the following cost?

Show all answers to 2 decimal places (2 d.p)

EDDIE SAYS
Start with 45 ÷ 12 = £3.75 for one litre of paint. The take £3.75 and multiply up by 3, 5, 8 and 22 Not sure about that colour of paint though....
• Question 4

If 8 of the same DVD's cost £96, how many DVD's can be bought for £60?

5
EDDIE SAYS
This is just a little added extra that you are sometimes asked for. £96 ÷ 8 = 12 This time you know the amount spent and you have to work backwards to find the number of DVDs. So instead of a multiplication, divide instead. £60 ÷ 12 = 5 As long as those DVDs are not horror films, I don't want to spend all night hiding behind the sofa..
• Question 5

Mindy buys 12 pens for  £7.80 and 6 note books for  £10.50.  How much does Mindy pay altogether for 7 pens and 4 note books?

£11.55
EDDIE SAYS
£7.80 ÷ 12 = £0.65 £10.50 ÷ 6 = £1.75 £0.65 x 7 = £4.55 £1.75 x 4 = £7.00
• Question 6

Here is a recipe for a fruit cake that serves 6 people.

175 g dried fruit

50 g candied peel

120 ml water

175 g butter

180 g caster sugar

3 large eggs

450 g flour

How much flour is required for  a cake to feed 11 people?

How many eggs are required for a cake to feed 16 people?

EDDIE SAYS
Flour 450g ÷ 6 = 75g 75 x 11 =825g Eggs 3 ÷ 6 = 0.5 0.5 x 16 = 8 Be careful not to get the division the wrong way round, easy done on questions such as this. Probably because you are thinking about cake..
• Question 7

Tracey changed £50 into dollars for her holiday to America.  The exchange rate was £1 = \$1.55

How many dollars did Tracey have at the start of her holiday?

Tracy came back with \$30.  How much did she get back in Pounds?

EDDIE SAYS
This skill is useful to know when converting currency. I am always excited to go on holiday. I think of it as my X factor moment. This reminds me to multiply when converting from Pounds to foreign currency. Coming home is not so nice so I have to do the opposite of my x factor and so divide when converting foreign currency back to pounds. £50 x 1.55 = \$77.50 \$30 ÷ 1.55 = £19.35
• Question 8

A lorry uses 35 litres of fuel to travel 250 km.

EDDIE SAYS
250 ÷ 35 = 7.14 km per litre 7.14 x 50 = 357 (to the nearest litre. 400 ÷ 7.14 = 56 I wouldn't mind having a go at driving a lorry.
• Question 9

A farm shop sells apples for £9 for a 12.5kg bag.

The same apples cost £1.83 for a 2.5kg bag at the supermarket.

Where are the apples better value, at the farm shop or the supermarket?

Farm Shop
EDDIE SAYS
Farm shop £9.00 ÷ 12.5 = £0.72 Supermarket £1.83 ÷ 2.5 = 0.732 Apples are a penny cheaper at the farm shop. You must like apples to buy them in that quantity.
• Question 10

The Coffee Cabin sells coffee in three different size cups.

£2.25 for 175 ml

£2.75 for 250 ml

£375 for 300 ml

Which size cup of coffee is the best value for money?

250 ml
EDDIE SAYS
£2.25 ÷ 175 = 0.0128p per ml £2.75 ÷ 250 = 0.011p per ml £3.75 ÷ 300 = 0.0125p per ml The best value for money is the 250 ml because it works out the cheapest per ml. Can I have a biscuit with mine?
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